Learn English – Is “giddy” derived from “Gid” which was Middle English for “God”

Ah, I see I should have read more closely.
I actually did some research that touches on this.

The ST- assonance (initial consonant cluster) has a long and varied and surprisingly coherent phonosemantic history, dating from a pre-Proto-Indo-European era.

I tripped over ST- while trying to figure out what style meant, in a paper on metaphors, for a literary journal named Style. As usual, there was a lot more stuff going on than I had expected.

The paper is called "Style Stands Still", and I see no reason to reproduce it here, since it's online. (The stuff about ST- starts on page 8, but it's built on the context of the first part; the paper is 20 pages long, with bibliography).

EDIT: By request, a brief excerpt from the paper:

Figure 1. st-initial PIE roots, with some reflexes in Modern English
Source: Watkins (2000), Pokorny (1959)

• *stā- ‘To stand, with derivatives meaning “place or thing that is standing”’ (Pok sta- 1004)
  style, stand, steed, stud, stay, stage, stamen, standard, stem, station, stasis, static, status, stable, stoic, store, stylite, steer
• *steigh- ‘To stride, step, rise’ (Pok steigh- 1017)
  stile, stirrup, stickle, distich, acrostic
• *steu- ‘To push, stick, knock, beat’ (Pok 2. steu- 1025)
  stub, steeple, stoop, stutter, stock, stoke, steep
• *stel- ‘To put, stand; with derivatives referring to a standing object or place’ (Pok 3. stel- 1019)
  stolon, stalk, stele, stilt, pedestal, stolid, stall, stout
• *ster- ‘Stiff’ (Pok 5. ster- 1029)
  stare, starch, stork, starve, stark, stern, strut, start, stark, startle
• *stebh- ‘Post, stem; to support, place firmly on, fasten’ (Pok steb(h)- 1011)
  stoop, staff, staple, stump, stamp, stomp, stave
• *steip- ‘To stick, compress’ (Pok steib(h)- 1015)
  stubble, stiff, stipple
• *steg- ‘Pole, stick’ (Pok 2. (s)teg- 1014)
  stake, stack, stagger
• *stegh- ‘To stick, prick; pointed’ (Pok stegh- 1014)
  stair, stick, sting, stigma, stimulate, stag

There is a strong family resemblance among the roots here. Indeed, on perusing this list, one finds a persistent cognitive image building up, with at least the following four significant perceptual properties:

Figure 2. Cognitive semantic properties of st-initial PIE roots

1. One-Dimensional: The image has only one salient major dimension
2. Vertical: That dimension is situated in an up-and-down orientation
3. Strong: The image displays rigidity, stability, and physical integrity
4. Still: The image is either unmoving, or frozen in motion

...

Not all of the characteristics in Figure 2 will be true of every Modern English word that comes from the roots in Figure 1, but some combination of the features applies to them all. For instance, although the Modern English words stamen, stile, steeple, stalk, stork, staff, stake, and stick each come from a different PIE root, all of them refer either to long rigid objects or to things characterized by such, mostly vertically oriented, and often supporting, attached, or applied to other structures by their ends. For that matter, they tend to apply to any Modern English word beginning with st-, no matter where it comes from.

From the OED in relation to swallow (the bird):

swallow ▪ I.swallow, n.1 (ˈswɒləʊ) Forms: 1 s(u)ualu(u)ae, swealwe, swalowe, -uwe, -awe, 1, 4 swalewe, swalwe, swolwe, 4 swalugh, swalu, 4–6 swalow(e, 5 swalue, sualowe, 5–7 swallowe, 6– swallow. [Com. Teut. (not recorded for Gothic): OE. swealwe wk. fem. = OS. suala, MLG. swalewe, swalue, MDu. swâluwe, -ewe (Du. zwaluw), OHG. swalawa, swalwa (MHG. swal(e)we, G. schwalbe), ON. svala for *svǫlva (MSw., Sw. svala, Da. svale):—OTeut. *swalwōn-, the etymological meaning of which is disputed.

Continental Germanic dialects have also forms of other types: without w in the final syllable, e.g. MHG. swal, swale, MLG. swale, WFris. sweal, swel; with m-suffix, e.g. HG. (local) schwalm, schwalme, Flem. swaelem; forms with dim. suffix are widespread in LG. and Fris., e.g. MLG. swalike, swal(e)ke, LG. swaalke, Flem. swalcke (Kilian), EFris., NFris. swâlk, WFris. swealtsje, sweltsje.]

1. a. A bird of the genus Hirundo, esp. H. rustica, a well-known migratory bird with long pointed wings and forked tail, having a swift curving flight and a twittering cry, building mud-nests on buildings, etc., and popularly regarded as a harbinger of summer (cf. c). a 700 Epinal Gloss. 498 Hirundo, sualuuae. c 950 Guthlac x. (1909) 143 Þa comon þær sæmninga in twa swalewan fleoᵹan, and hi..heora sang upahofon. c 1000 Sax. Leechd. II. 156 Ᵹenim swealwan, ᵹebærn..to ahsan. Ibid. III. 44 Ᵹenim swolwan nest. c 1320 Sir Tristr. 1366 A swalu ich herd sing. c 1374 Chaucer Troylus ii. 64 The swalwe Proigne, with a sorwful lay,..gan make hir weymentinge. 1398 Trevisa Barth. De P.R. xii. xxii. (Bodl. MS.) lf. 122 b/1 In making of nestes þe swalowe is moste sliȝe. a 1450 Knt. de la Tour lxxx. 102 The dunge of swalues fell into the eyen of this good man Tobie. a 1529 Skelton P. Sparowe 404 The chattrynge swallow. 1579 Spenser Sheph. Cal. Mar. 11 The Swallow peepes out of her nest. 1611 Shakes. Wint. T. iv. iv. 119 Daffadils, That come before the Swallow dares...

I suspect the reference to the Old Teutonic swalwōn- by the OED, and its comment that the etymological meaning 'is disputed' might be a reference to Kluge's 1891 'An Etymological Dictionary of The German Language'.

Kluge has this to say:

No certain explanation can be given of the primary form swalwôn, f.; perhaps it represents swalgwôn-, pre-Teutonic swalkuân, to which Greek ἅλκύων is also traced.

Noting that ἅλκύων is Greek for halcyon, or kingfisher. All of this leaves me better informed, but none the wiser. There's more to be told about the pre-Teutonic roots perhaps and the link with that Greek word.